Stability of Peakons for the Generalized Camassa-Holm Equation

Abstract

We study the existence of minimizers for a constrained variational problems in H1(R). These minimizers are stable waves solutions for the Generalized Camassa-Holm equation, and their derivative may have a singularity (in which case the travelling wave is called a peakon). The existence result is based on a method developed by the same author in a previous work. By giving examples, we show how our method works.